Why my spot lights do not work properly?
From your screenshot, your lamp is only rated as outputting 1 Watt of power. You are effectively trying to illuminate your scene with around 6 Watts of power - 1/10th of a 60W lightbulb, presumably at many metres (Blender Units) range - so your scene is almost completely dark.
You need to simply increase the output of those lamps to more reasonable levels - eg, 600 Watts per lamp would be more reasonable.
I suspect you have gotten into this situation by duplicating the original Sun lamp and changing its type to 'Spot' without changing its output. Note that Sun lamps are rated in 'Strength' - with a strength of '1' equating to 1 'Sun' (our sun) - but Spot lamps are rated in 'Power' (in Watts). When you change the lamp type the Strength gets changed to Power but the value remains the same (so 1 'Sun' gets changed into a 1W lamp). When changing between types, always check the other settings to ensure they are still reasonable for your situation.
In summary, increase the output from your lamps.